Interim Looks Research Articles

An automated platform trial framework for A/B testing

This paper proposes a platform trial for conducting A/B tests with multiple arms and interim monitoring to investigate the impact of several factors on the expected sample size and probability of early stopping. We examined the performance of three stopping boundaries: O’Brien Fleming (OBF) stopping for either futility or difference (both), Pocock stopping for futility only, and fixed sample size design. We simulated twelve scenarios of different orders of arms based on various effect sizes, as well as considered 1 or 3 interim looks. The overall findings are summarizing in a flowchart to provide intuitive guidance for the design of the platform based on the simulation. We found that it is better to use OBF stopping for both if there is any effective variant and the trial is sufficiently powered to detect the expected effect size. If the study is underpowered to detect a difference, we recommend fixed sample size design to gather as much information as possible, however if the expected sample size is important to minimize, we recommend using Pocock boundaries with futility monitoring. Our results aimed at helping high-tech companies conduct their own studies without requiring extensive knowledge of clinical trial design and statistical methodology.

Addressing the Evidence Gap in Aneurysmal Subarachnoid Hemorrhage: The Need for a Pragmatic Randomized Trial Platform.

Aneurysmal subarachnoid hemorrhage (aSAH) occurs less often than other stroke types but affects younger patients, imposing a disproportionately high burden of long-term disability. Although management advances have improved outcomes over time, relatively few aSAH treatments have been tested in randomized clinical trials (RCTs). One lesson learned from COVID-19 is that trial platforms can facilitate the efficient execution of multicenter RCTs even in complex diseases during challenging conditions. An aSAH trial platform with standardized eligibility criteria, randomization procedures, and end point definitions would enable the study of multiple targeted interventions in a perpetual manner, with treatments entering and leaving the platform based on predefined decision algorithms. An umbrella institutional review board protocol and clinical trial agreement would allow individual arms to be efficiently added as amendments rather than stand-alone protocols. Standardized case report forms using the National Institutes of Health/National Institute of Neurological Disorders and Stroke common data elements and general protocol standardization across arms would create synergies for data management and monitoring. A Bayesian analysis framework would emphasize frequent interim looks to enable early termination of trial arms for futility, common controls, borrowing of information across arms, and adaptive designs. A protocol development committee would assist investigators and encourage pragmatic designs to maximize generalizability, reduce site burden, and execute trials efficiently and cost-effectively. Despite decades of steady clinical progress in the management of aSAH, poor patient outcomes remain common, and despite the increasing availability of RCT data in other fields, it remains difficult to perform RCTs to guide more effective care for aSAH. The development of a platform for pragmatic RCTs in aSAH would help close the evidence gap between aSAH and other stroke types and improve outcomes for this important disease with its disproportionate public health burden.

MUCE: Bayesian hierarchical modelling for the design and analysis of phase 1b multiple expansion cohort trials

AbstractWe propose a multiple cohort expansion (MUCE) approach as a design or analysis method for phase 1b multiple expansion cohort trials, which are novel first-in-human studies conducted following phase 1a dose escalation. In a phase 1b expansion cohort trial, one or more doses of a new investigational drug identified from phase 1a are tested for initial antitumour activities in patients with different indications (cancer types and/or biomarker status). Each dose–indication combination defines an arm, and patients are enrolled in parallel cohorts to all the arms. The MUCE design is based on a class of Bayesian hierarchical models that adaptively borrow information across arms. Specifically, we employ a latent probit model that allows for different degrees of borrowing across doses and indications. Statistical inference is directly based on the posterior probability of each arm being efficacious, facilitating the decision making that decides which arm to select for further testing. The MUCE design also incorporates interim looks, based on which the nonpromising arms will be stopped early due to futility. Through simulation studies, we show that MUCE exhibits superior operating characteristics. We also compare the performance of MUCE with that of Simon’s two-stage design and some existing Bayesian designs for multiarm trials. To our knowledge, MUCE is the first Bayesian method for phase 1b expansion cohort trials with multiple doses and indications.

Group sequential designs for cancer immunotherapy trial with delayed treatment effect

ABSTRACT Cancer immunotherapy trials are frequently characterized by delayed treatment effects such that the proportional hazards assumption is violated and the log-rank test suffers a substantial loss of statistical power. To increase the efficacy of the trial design, a variety of weighted log-rank tests have been proposed for fixed sample and group sequential trial designs. However, in such a group sequential design, it is often not recommended for futility interim monitoring due to possible delayed treatment effect which could result a high false-negative rate. To resolve this problem, we propose a group sequential design using a piecewise weighted log-rank test which provides an event-driven approach based on number of events after the delayed time. That is, the interim looks will not be conducted until the planned number of events observed after the delay time. Thus, it avoids the possibility of false-negative rate due to the delayed treatment effect. Furthermore, with an event-driven approach, the proposed group sequential design is robust against the underlying survival, accrual and censoring distributions. The group sequential designs using Fleming-Harrington-( ρ , γ ) weighted log-rank test and a new weighted log-rank test are also discussed.

Online control of the False Discovery Rate in group-sequential platform trials.

When testing multiple hypotheses, a suitable error rate should be controlled even in exploratory trials. Conventional methods to control the False Discovery Rate assume that all p-values are available at the time point of test decision. In platform trials, however, treatment arms enter and leave the trial at different times during its conduct. Therefore, the actual number of treatments and hypothesis tests is not fixed in advance and hypotheses are not tested at once, but sequentially. Recently, for such a setting the concept of online control of the False Discovery Rate was introduced. We propose several heuristic variations of the LOND procedure (significance Levels based On Number of Discoveries) that incorporate interim analyses for platform trials, and study their online False Discovery Rate via simulations. To adjust for the interim looks spending functions are applied with O'Brien-Fleming or Pocock type group-sequential boundaries. The power depends on the prior distribution of effect sizes, for example, whether true alternatives are uniformly distributed over time or not. We consider the choice of design parameters for the LOND procedure to maximize the overall power and investigate the impact on the False Discovery Rate by including both concurrent and non-concurrent control data.

A randomized Bayesian optimal phase II design with binary endpoint

ABSTRACT In this paper, we propose a randomized Bayesian optimal phase II (RBOP2) design with a binary endpoint (e.g., response rate). A beta-binomial distribution is used to model the binary endpoint for a two-arm phase II trial. Posterior probabilities of the endpoint of interest are evaluated at each interim look and used in the decision to stop the trial due to futility. Compared with other Bayesian designs, the proposed RBOP2 design has the following merits: (i) strongly controls the type I error rate at a pre-defined level; (ii) optimizes the stopping boundaries, thus maximizing the power to detect treatment effects and minimizing the expected sample size for futile treatment; (iii) does not limit the number of interim looks, thus enabling frequent trial monitoring; and (iv) allows the stopping boundaries to be pre-defined in the protocol and is easy to implement. We conduct simulation studies to compare the proposed design with a group sequential design and other Bayesian randomized designs and evaluate its operating characteristics under different scenarios.

Adaptive design with bayesian informed interim decisions: application to a randomized trial of mechanical circulatory support

Abstract Background Cardiovascular trials increasingly require large sample sizes and long follow-up periods. Several approaches have been developed to optimize sample size such as adaptive group sequential trials, samples size re-estimation based on the promising zone, and the win ratio. Traditionally, the log-rank or the Cox proportional hazards model is used to test for treatment effects, based on a constant hazard rate and proportional hazards alternatives, which however, may not always hold. Large sample sizes and/or long follow up periods are especially challenging for trials evaluating the efficacy of acute care interventions. Purpose We propose an adaptive design wherein using interim data, Bayesian computation of predictive power guides the increase in sample size and/or the minimum follow-up duration. These computations do not depend on the constant hazard rate and proportional hazards assumptions, thus yielding more robust interim decision making for the future course of the trial. Methods PROTECT IV is designed to evaluate mechanical circulatory support with the Impella CP device vs. standard of care during high-risk PCI. The primary endpoint is a composite of all-cause death, stroke, MI or hospitalization for cardiovascular causes with initial minimum follow-up of 12 months and initial enrolment of 1252 patients with expected recruitment in 24 months. The study will employ an adaptive increase in sample size and/or minimum follow-up at the Interim analysis when ∼80% of patients have been enrolled. The adaptations utilize extensive simulations to choose a new sample size up to 2500 and new minimal follow-up time up to 36 months that provides a Bayesian predictive power of 85%. Bayesian calculations are based on patient-level information rather than summary statistics therefore enabling more reliable interim decisions. Constant or proportional hazard assumptions are not required for this approach because two separate Piece-wise Constant Hazard Models with Gamma-priors are fitted to the interim data. Bayesian predictive power is then calculated using Monte-Carlo methodology. Via extensive simulations, we have examined the utility of the proposed design for situations with time varying hazards and non-proportional hazards ratio such as situations of delayed treatment effect (Figure) and crossing of survival curves. The heat map of Bayesian predictive power obtained when the interim Kaplan-Meier curves reflected delayed response shows that for this scenario an optimal combination of increased sample size and increased follow-up time would be needed to attain 85% predictive power. Conclusion A proposed adaptive design with sample size and minimum follow-up period adaptation based on Bayesian predictive power at interim looks allows for de-risking the trial of uncertainties regarding effect size in terms of control arm outcome rate, hazard ratio, and recruitment rate. Funding Acknowledgement Type of funding sources: Private company. Main funding source(s): Abiomed, Inc Figure 1

A simulation-based comparison of estimation methods for adaptive and classical group sequential clinical trials.

Statistical methods for controlling the type-I error of hypothesis tests in adaptive group sequential clinical trials are well established and well understood. However, methods for obtaining statistically valid point estimates and confidence intervals for adaptive designs are not as well established or as well understood. At the end of an adaptive trial, one may calculate the repeated confidence interval (RCI), which provides conservative coverage of , or the backward image confidence interval (BWCI), which provides exact coverage of and is an extension of the stagewise adjusted confidence interval (SWCI, used in classical group sequential designs). The BWCI can also provide a median unbiased estimate (MUE) of . There is a need to better understand the coverage and possible biases associated with these methods. We conducted a simulation study exploring parameter estimation following sample size reestimation based on testing methods with strong control of type-I error. Generally, the BWCI provided exact coverage, the naïve CI provided inconsistent coverage, and the RCI provided conservative coverage. Additionally, we note considerable asymmetry in the coverage from above/from below for the RCI, although we did not see any instance where the 95% RCI excluded the true parameter more than 2.5% on either side. At the end of an adaptive group sequential trial, we strongly recommend the use of the BWCI (and associated MUE), with the RCI computed during interim looks; the naïve CI should be avoided. These results and conclusions also hold true for classical group sequential designs.

Adaptive design with bayesian informed interim decisions: application to a randomized trial of mechanical circulatory support

Abstract Background Cardiovascular trials increasingly require large sample sizes and long follow-up periods. Several approaches have been developed to optimize sample size such as adaptive group sequential trials, samples size re-estimation based on the promising zone, and the win ratio. Traditionally, the log-rank or the Cox proportional hazards model is used to test for treatment effects, based on a constant hazard rate and proportional hazards alternatives, which however, may not always hold. Large sample sizes and/or long follow up periods are especially challenging for trials evaluating the efficacy of acute care interventions. Purpose We propose an adaptive design wherein using interim data, Bayesian computation of predictive power guides the increase in sample size and/or the minimum follow-up duration. These computations do not depend on the constant hazard rate and proportional hazards assumptions, thus yielding more robust interim decision making for the future course of the trial. Methods PROTECT IV is designed to evaluate mechanical circulatory support with the Impella CP device vs. standard of care during high-risk PCI. The primary endpoint is a composite of all-cause death, stroke, MI or hospitalization for cardiovascular causes with initial minimum follow-up of 12 months and initial enrolment of 1252 patients with expected recruitment in 24 months. The study will employ an adaptive increase in sample size and/or minimum follow-up at the Interim analysis when ∼80% of patients have been enrolled. The adaptations utilize extensive simulations to choose a new sample size up to 2500 and new minimal follow-up time up to 36 months that provides a Bayesian predictive power of 85%. Bayesian calculations are based on patient-level information rather than summary statistics therefore enabling more reliable interim decisions. Constant or proportional hazard assumptions are not required for this approach because two separate Piece-wise Constant Hazard Models with Gamma-priors are fitted to the interim data. Bayesian predictive power is then calculated using Monte-Carlo methodology. Via extensive simulations, we have examined the utility of the proposed design for situations with time varying hazards and non-proportional hazards ratio such as situations of delayed treatment effect (Figure) and crossing of survival curves. The heat map of Bayesian predictive power obtained when the interim Kaplan-Meier curves reflected delayed response shows that for this scenario an optimal combination of increased sample size and increased follow-up time would be needed to attain 85% predictive power. Conclusion A proposed adaptive design with sample size and minimum follow-up period adaptation based on Bayesian predictive power at interim looks allows for de-risking the trial of uncertainties regarding effect size in terms of control arm outcome rate, hazard ratio, and recruitment rate. Funding Acknowledgement Type of funding sources: Private company. Main funding source(s): Abiomed, Inc Figure 1

A Sequential Predictive Power Design for a COVID Vaccine Trial

Medical investigations for therapeutics and vaccines for combating a pandemic such as COVID-19, call for flexible and adaptive trial designs that are capable of producing robust results amidst uncertainties. Here, we present a Bayesian sequential design to study the efficacy of Bacillus Calmette–Guérin (BCG) in providing protection against COVID-19 infections via its known “trained-immunity” mechanism. The main design consideration is to provide a framework to rapidly establish a proof-of-concept on the vaccine efficacy of BCG under a constantly evolving incidence rate and in the absence of prior efficacy data. The trial design is based on taking several interim looks and calculating the predictive power with the current cohort at each interim look. Decisions to stop the trial for futility or stopping enrollment for efficacy are made based on the current cohort predictive power computation. At any interim, if any of the above decisions cannot be taken then the study continues to enroll till the next interim look. Via extensive numerical studies, we show that the proposed design can achieve the desired frequentist operating characteristics, currently required by regulatory bodies while offering greater flexibility in terms of sample size and the ability to make robust interim decisions.

On information fraction for Fleming‐Harrington type weighted log‐rank tests in a group‐sequential clinical trial design

When comparing survival times of treatment and control groups under a more realistic nonproportional hazards scenario, the standard log-rank (SLR) test may be replaced by a more efficient weighted log-rank (WLR) test, such as the Fleming-Harrington (FH) test. Designing a group-sequential clinical trial with one or more interim looks during which a FH test will be performed, necessitates correctly quantifying the information fraction (IF). For SLR test, IF is defined simply as the ratio of interim to final numbers of events; but for FH test, it can deviate substantially from this ratio. In this article, we separate the effect of weight function (of FH test) alone on IF from the effect of censoring. We have shown that, without considering the effect of censoring, IF can be derived analytically for FH test using information available at the design stage and the additional effect due to censoring is relatively smaller. This article intends to serve two major purposes: first, to emphasize and rationalize the deviation of IF in weighted log-rank test from that of SLR test which is often overlooked (Jiménez, Stalbovskaya, and Jones); second, although it is impossible to predict IF for a weighted log-rank test at the design stage, our decomposition of effects on IF provides a reasonable and practically feasible range of IF to work with. We illustrate our approach with an example and provide simulation results to evaluate operating characteristics.

Herd immunity for COVID-19

Herd immunity for COVID-19

Bayesian optimal phase II clinical trial design with time‐to‐event endpoint

We propose a Bayesian optimal phase II (BOP2) design for clinical trials with a time-to-event endpoint (eg, progression-free survival [PFS]) or co-primary endpoints consisted of a time-to-event endpoint and a categorical endpoint (eg, PFS and toxicity). We use an exponential-inverse gamma model to model the time to event. At each interim, the go/no-go decision is made by comparing the posterior probabilities of the event of interest with an adaptive probability cutoff. The BOP2 design is flexible in the number of interim looks and applicable to both single-arm and two-arm trials. The design maximizes the power for detecting effective treatments, with a well-controlled type I error, thereby bridging the gap between Bayesian designs and frequentist designs. The BOP2 design is easy to implement. Its stopping boundary can be enumerated and included in study protocol before the onset of the trial for single-arm studies. Simulation studies show that the BOP2 design has favorable operating characteristics, with higher power and lower risk of incorrectly terminating the trial than some Bayesian phase II designs. The software to implement the BOP2 design will be freely available at www.trialdesign.org.

An Empirical Investigation of Bayesian Clinical Trial Design in Metastatic Breast Cancer.

Over the past 20years, there has been increasing interest in the use of Bayesian statistical methods for the analysis of clinical trials used to support regulatory decisions. Bayesian methods for the analysis of clinical trials are an attractive option when good prior information is available. Yet, in many cases, prior information is scarce and only tentative or proprietary prior information exists. In these situations, it is necessary to use noninformative type or skeptical-type priors. We undertook a systematic study of Bayesian methods and applied them to 13 randomized clinical trials in metastatic breast cancer submitted to the U.S. Food and Drug Administration for registrational purposes. Across all 13 studies, there were a total of 10,521 patients using 10 experimental agents. Our results demonstrated that Bayesian analyses with noninformative priors provided similar results to more traditional analyses. We also found that early interim looks at the study results can vary widely based upon the type of prior used. Finally, we found that pre-defined threshold stopping rules need to be relatively strong to prevent trials from stopping very early. Our results suggest that, when prior information is limited and a noninformative prior is used, there is little numerical difference between Bayesian methods and more traditional analysis methods. Bayesian methods, however, may provide additional summaries of the data that are more easily interpretable than means and confidence intervals.

Optimizing interim analysis timing for Bayesian adaptive commensurate designs.

In developing products for rare diseases, statistical challenges arise due to the limited number of patients available for participation in drug trials and other clinical research. Bayesian adaptive clinical trial designs offer the possibility of increased statistical efficiency, reduced development cost and ethical hazard prevention via their incorporation of evidence from external sources (historical data, expert opinions, and real-world evidence), and flexibility in the specification of interim looks. In this paper, we propose a novel Bayesian adaptive commensurate design that borrows adaptively from historical information and also uses a particular payoff function to optimize the timing of the study's interim analysis. The trial payoff is a function of how many samples can be saved via early stopping and the probability of making correct early decisions for either futility or efficacy. We calibrate our Bayesian algorithm to have acceptable long-run frequentist properties (Type I error and power) via simulation at the design stage. We illustrate our approach using a pediatric trial design setting testing the effect of a new drug for a rare genetic disease. The optimIA R package available at https://github.com/wxwx1993/Bayesian_IA_Timing provides an easy-to-use implementation of our approach.

Highly Efficient Clinical Trials Simulator (HECT): Software application for planning and simulating platform adaptive trials

Background: Adaptive designs and platform designs are among two common clinical trial innovations that are increasingly being used to manage medical intervention portfolios and attain faster regulatory approvals. Planning of adaptive and platform trials necessitate simulations to understand how a set of adaptation rules will likely affect the properties of the trial. Clinical trial simulations, however, remain a black box to many clinical trials researchers who are not statisticians. Results: In this article we introduce a simple intuitive open-source browser-based clinical trial simulator for planning adaptive and platform trials. The software application is implemented in RShiny and features a graphical user interface that allows the user to set key clinical trial parameters and explore multiple scenarios such as varying treatment effects, control response and adherence, as well as number of interim looks and adaptation rules. The software provides simulation options for a number of designs such as dropping treatment arms for futility, adding a new treatment arm (i.e., platform design), and stopping a trial early based on superiority. All available adaptations are based on underlying Bayesian probabilities. The software comes with a number of graphical outputs to examine properties of individual simulated trials. The main output is a comparison of trial design performance across several simulations, graphically summarizing type I error (false positive risk), power, and expected cost/time to completion of the considered designs. Conclusion: We have developed and validated an intuitive highly efficient clinical trial simulator for planning of clinical trials. The software is open-source and caters to clinical trial investigators who do not have the statistical capacity for trial simulations available in their team. The software can be accessed via any web browser via the following link: https://mtek.shinyapps.io/hect/

TOP: Time-to-Event Bayesian Optimal Phase II Trial Design for Cancer Immunotherapy.

Immunotherapies have revolutionized cancer treatment. Unlike chemotherapies, immune agents often take longer to show benefit, and the complex and unique mechanism of action of these agents renders the use of multiple endpoints more appropriate in some trials. These new features of immunotherapy make conventional phase II trial designs, which assume a single binary endpoint that is quickly ascertainable, inefficient and dysfunctional. We propose a flexible and efficient time-to-event Bayesian optimal phase II (TOP) design. The TOP design is efficient in that it allows real-time "go/no-go" interim decision making in the presence of late-onset responses by using all available data and maximizes statistical power for detecting effective treatments. TOP is flexible in the number of interim looks and capable of handling simple and complicated endpoints under a unified framework. We conduct simulation studies to evaluate the operating characteristics of the TOP design. In the considered trial settings, compared to some existing Bayesian designs, the TOP design shortens the trial duration by 4-10 months and improves the power to detect effective treatment up to 90%, with well-controlled type I errors. The TOP design is transparent and easy to implement, as its decision rules can be tabulated and included in the protocol prior to the conduct of the trial. The TOP design provides a flexible, efficient, and easy-to-implement method to accelerate and improve the development of immunotherapies.

Highly Efficient Clinical Trials Simulator (HECT): Software application for planning and simulating platform adaptive trials.

Background: Adaptive designs and platform designs are among two common clinical trial innovations that are increasingly being used to manage medical intervention portfolios and attain faster regulatory approvals. Planning of adaptive and platform trials necessitate simulations to understand how a set of adaptation rules will likely affect the properties of the trial. Clinical trial simulations, however, remain a black box to many clinical trials researchers who are not statisticians. Results: In this article we introduce a simple intuitive open-source browser-based clinical trial simulator for planning adaptive and platform trials. The software application is implemented in RShiny and features a graphical user interface that allows the user to set key clinical trial parameters and explore multiple scenarios such as varying treatment effects, control response and adherence, as well as number of interim looks and adaptation rules. The software provides simulation options for a number of designs such as dropping treatment arms for futility, adding a new treatment arm (i.e., platform design), and stopping a trial early based on superiority. All available adaptations are based on underlying Bayesian probabilities. The software comes with a number of graphical outputs to examine properties of individual simulated trials. The main output is a comparison of trial design performance across several simulations, graphically summarizing type I error (false positive risk), power, and expected cost/time to completion of the considered designs. Conclusion: We have developed and validated an intuitive highly efficient clinical trial simulator for planning of clinical trials. The software is open-source and caters to clinical trial investigators who do not have the statistical capacity for trial simulations available in their team. The software can be accessed via any web browser via the following link: https://mtek.shinyapps.io/hect/.

Highly Efficient Clinical Trials Simulator (HECT): Software application for planning and simulating platform adaptive trials

Background: Adaptive designs and platform designs are among two common clinical trial innovations that are increasingly being used to manage medical intervention portfolios and attain faster regulatory approvals. Planning of adaptive and platform trials necessitate simulations to understand how a set of adaptation rules will likely affect the properties of the trial. Clinical trial simulations, however, remain a black box to many clinical trials researchers who are not statisticians. Results: In this article we introduce a simple intuitive open-source browser-based clinical trial simulator for planning adaptive and platform trials. The software application is implemented in RShiny and features a graphical user interface that allows the user to set key clinical trial parameters and explore multiple scenarios such as varying treatment effects, control response and adherence, as well as number of interim looks and adaptation rules. The software provides simulation options for a number of designs such as dropping treatment arms for futility, adding a new treatment arm (i.e., platform design), and stopping a trial early based on superiority. All available adaptations are based on underlying Bayesian probabilities. The software comes with a number of graphical outputs to examine properties of individual simulated trials. The main output is a comparison of trial design performance across several simulations, graphically summarizing type I error (false positive risk), power, and expected cost/time to completion of the considered designs. Conclusion: We have developed and validated an intuitive highly efficient clinical trial simulator for planning of clinical trials. The software is open-source and caters to clinical trial investigators who do not have the statistical capacity for trial simulations available in their team. The software can be accessed via any web browser via the following link: https://mtek.shinyapps.io/hect/

Interim monitoring using the adaptively weighted log-rank test in clinical trials for survival outcomes.

For testing treatment effect with survival data, the log-rank test has been the method of choice and enjoys an optimality property under proportional hazards alternatives. However, there can be significant loss of power in a variety of nonproportional situations. Yang and Prentice proposed an adaptively weighted log-rank test that improves the power of the log-rank test over a wide range of hazard ratio scenarios. In clinical trials, the data and safety monitoring board typically monitors the trial results periodically. Here, we develop interim testing procedures for the adaptively weighted log-rank test. We establish the asymptotic distribution of the test statistics at the interim looks and use a resampling method to obtain the stopping boundaries. Through examination of the test behavior under local alternatives, we show that the adaptively weighted log-rank test is fully efficient when the limiting censoring distributions in the two groups are equal. Unlike the case for the usual application of the log-rank test, critical values obtained from the resampling method are asymptotically valid without the assumption of equal censoring distributions in the two groups. Extensive simulation studies show that the new method improves the log-rank test for a wide range of treatment effect patterns, and that the resampling approach yields better control of the type 1 error rate than the originally proposed approach in the work of Yang and Prentice. The new procedures are illustrated in several clinical trial examples.